In the background of the Lifshitz black hole with linear axion field and hyperscaling violating factor, the axion field was shown with the same phenomenon. The lower half-plane pole-skipping points at negative integer (imaginary) Matsubara frequencies. When \(\theta =0\) , \(z=1\) , \(Q=0\)  and \(\beta =0\) , the metric (REF ) recovers the AdS\(_4\)  black brane solution. The location of the first order pole-skipping point is the same as that of ref.[1]}, [2]}. We also compare the lower half-plane pole-skipping points with hydrodynamic poles show that the hydrodynamic dispersion relation passes through pole-skipping points when \(\mathfrak {w}, \mathfrak {k}\rightarrow 0\) .
